Question

In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q R and S. If AP = 6 cm, BP = 5 cm, CQ = 3 cm and DR = 4 cm then perimeter of quad. ABCD is ______.

Options

• 18 cm

• 27 cm

• 36 cm

• 32 cm

Answer 1

In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q R and S. If AP = 6 cm, BP = 5 cm, CQ = 3 cm and DR = 4 cm then perimeter of quad. ABCD is 36 cm.

Explanation:

Tangents from the same vertex to a circle are equal in length.

AB = AP + BP

= 6 + 5

= 11 cm

From B, BQ = BP = 5,

So BC = BQ + CQ

= 5 + 3

= 8 cm

From C, CR = CQ = 3,

So CD = CR + DR 

= 3 + 4

= 7 cm

From A, AS = AP = 6 and from D,

SD = DR = 4,

So AD = AS + SD 

= 6 + 4

= 10 cm

Perimeter = AB + BC + CD + DA

= 11 + 8 + 7 + 10

= 36 cm